Kirsten Gillibrand has called on the president to resign.
Photograph: Jim Lo Scalzo/EPA

Donald Trump claimed on Tuesday that the harassment accusations against him were a Democratic conspiracy as he lashed out at a prominent female senator with what she quickly dubbed a “sexist smear”.

The sexual misconduct allegations against Donald Trump – the full list

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“Lightweight Senator Kirsten Gillibrand, a total flunky for Chuck Schumer and someone who would come to my office ‘begging’ for campaign contributions not so long ago (and would do anything for them), is now in the ring fighting against Trump,” the president tweeted.

Gillibrand – who along with three male Democratic senators has called on Trump to resign over the numerous sexual misconduct accusations against him – responded on Twitter minutes later. “You cannot silence me or the millions of women who have gotten off the sidelines to speak out about the unfitness and shame you have brought to the Oval Office,” the New York senator wrote.

She added: “I will not be silenced on this issue. Neither will the women who stood up to the president yesterday, and neither will the millions of women who have been marching since the women’s march [in January] to stand up against policies they do not agree with.”

Trump singled out Gillibrand while ignoring the male senators who have also called on him to step down: the Vermont senator Bernie Sanders, the New Jersey senator Cory Booker and the Oregon senator Jeff Merkley.

The White House press secretary, Sarah Sanders, denied there were any sexual implications behind Trump’s tweet, telling reporters: “Only if your mind is in the gutter would you have read it that way.

“This is the same sentiment the president has expressed many times before when he has exposed corruption of the entire political system,” Sanders said. “This isn’t a new sentiment. This isn’t new terminology.

“He’s not alleging anything,” she added. “There’s no way that this is sexist at all.”

But the tweet drew swift condemnation from Democrats for its provocative innuendo, particularly against the backdrop of a national dialogue around sexual harassment against women.

Warren later characterized Trump’s tweet as “disgusting”, telling reporters on Capitol Hill: “It was clear what he was getting at. He is disgusting.”

House minority leader Nancy Pelosi also condemned Trump’s attack, saying it was “disgusting and disgraceful, and of course obviously not true”.

Trump’s comments came a day after three women who previously accused Trump of sexual harassment shared their stories in an interview on NBC and at a press conference in New York. While the White House has expressed a desire not to relitigate the accusations, the president’s outburst placed the conversation squarely back on his treatment of women.

A fourth accuser, Melinda McGillivray, appeared on NBC Tuesday morning to speak about her own sexual misconduct allegation against Trump.

McGillivray, who like the other women had initially shared her story during the 2016 campaign, accused Trump of groping her in 2003 at his Mar-a-Lago hotel in West Palm Beach, Florida. McGillivray said she was 23 at the time and photographing a concert at Trump’s property.

“The next thing I know, I feel a grab on my right side … to my surprise, it’s Donald,” McGillivray said on Megyn Kelly Today.

“He’s standing a foot and a half away from me, so he had to reach out and touch me. I stand there and I’m stunned. I don’t even know what to do with myself in that moment.”

At least 16 women have accused Trump of sexual assault. In many cases, the behavior they describe mirrors what Trump himself bragged about doing in a 2005 Access Hollywood tape leaked months before the November election. In the tape, Trump boasted of kissing and groping women without their consent.

Trump dismissed the claims in a tweet on Tuesday morning, suggesting – without evidence – that they were part by of a coordinated effort by Democrats to undermine his presidency.

But while Trump claimed not to know the women alleging misconduct, there was some photographic evidence to the contrary. Footage from the Apprentice shows Trump sitting across the table from Summer Zervos, a former contestant who said he groped her. Natasha Stoynoff, a former correspondent for People Magazine, was photographed with Trump at Mar-a-Lago on the same day she alleges he forcibly kissed her. Another photograph shows Trump and Jill Harth, who opened up to the Guardian last year about filing a lawsuit against him for “attempted rape” in 1997.

With the issue of sexual misconduct under a national spotlight, nearly 60 female lawmakers have formally requested a congressional investigation into Trump. In a letter, 56 female Democrats wrote to the House committee on oversight and government reform requesting an investigation. “We cannot ignore the multitude of women who have come forward with accusations against Mr Trump,” the Democratic Women’s Working Group wrote.

At a press conference Tuesday, the lawmakers lamented that while other powerful men from entertainment, media and politics had been held accountable for allegations of sexual misconduct, the complaints of Trump’s accusers had “fallen on deaf ears”.

“The #MeToo movement has arrived and sexual abuse will not be tolerated, whether it’s by a Hollywood producer, the chef of a restaurant, a member of Congress or the president of the United States,” said Lois Frankel, a representative from Florida who is the head of the working group.

Gillibrand’s office said she met with Trump once in 2010 and that his daughter, Ivanka, was also present for the meeting.

According to federal records, Trump donated $7,950 to Gillibrand’s House and Senate campaigns between 2007 and 2010. Ivanka Trump separately donated $2,000 to Gillibrand in 2014.